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SYLLABUS

UNIT-I

Solving Systems of Linear Equations, Eigen Values and Eigen Vectors Rank of a Matrix by Echelon Form and Normal Form - Solving System of Homogeneous and Non-Homogeneous Linear Equations - Gauss Elimination Method - Eigen Values and Eigen Vectors and Properties.

UNIT-II

Cayley-Hamilton Theorem and Quadratic Forms Cayley-Hamilton Theorem (Without Proof) - Applications - Finding the Inverse and Power of a Matrix by Cayley-Hamilton Theorem - Reduction to Diagonal Form - Quadratic Forms and Nature of the Quadratic Forms - Reduction of Quadratic Form to Canonical Forms by Orthogonal Transformation.

UNIT-III

Iterative Methods Introduction - Bisection Method - Secant Method - Method of False Position - Iteration Method - Newton-Raphson Method (One Variable and Simultaneous Equations) - Jacobi and Gauss-Seidel Methods for Solving System of Equations Numerically.

UNIT-IV

Interpolation Introduction - Errors in Polynomial Interpolation - Finite Differences - Forward Differences - Backward Differences - Central Differences - Relations Between Operators - Newton’s Forward and Backward Formulae for Interpolation - Interpolation with Unequal Intervals - Lagrange’s Interpolation Formula - Newton’s divided Difference Formula.

UNIT-V

Numerical Differentiation and Integration, Solution of Ordinary Differential Equations with Initial Conditions Numerical Differentiation Using Interpolating Polynomial - Trapezoidal Rule - Simpson’s 1/3rd and 3/8th Rule - Solution of Initial Value Problems by Taylor’s Series - Picard’s Method of Successive Approximations - Euler’s Method - Runge-Kutta Method (Second and Fourth Order).